Question

Two flat panes of glass (80 cm long, 15 cm wide, 4 mm thick) are on your lab table directly under a nearly monochromatic (wavelength 650 nm) light source. At one end one pane is resting on the other; at their other ends they are separated by a single thickness of paper. You notice that the light is strongly reflected only in multiple bands occurring one every 2.5 cm. How thick. is the paper?

Answer 1

$2t = 2\theta= m\lambda$    for a dark fringe

$2t = 2\theta= (2m+1)\lambda/2$    for a bright fringe

$\Delta x=L\frac{\lambda }{2t}$

$\Delta x=2.5cm=2.5\times 10^{-2}m$

$L=80cm=80\times 10^{-2}m$

$\lambda =650nm=650\times 10^{-9}m$

$\Delta x=L\frac{\lambda }{2t}\Rightarrow t=\frac{L\lambda }{2\Delta x}$

$t=\frac{L\lambda }{2\Delta x}$

$t=\frac{80\times 10^{-2}m\times 650\times 10^{-9}m}{2\times 2.5\times 10^{-2}m}$

$t=\frac{52\times 10^{-8}m^2}{5\times 10^{-2}m}=10.4\times 10^{-6}m$

$t=10.4\times \mu m$